I am trying to simulate lunar descent and landing as a part of my undergraduate project. For time being, I have included gravity turn guidance scheme and used these equations

Now, I can solve ODEs for flight path angle, velocity and altitude, integrate it with acceleration profile given by the guidance law and get corresponding profiles of altitude, velocity, and flight path angle for the landing sequence.

Currently, the program calculates circular orbit velocity at a given input altitude and de-orbits impulsively. It then initiates thrust command and lands unconstrained, controlling only, how and whether or not I land (altitude, velocity, fuel, flight path angle).

What is the most efficient way to include propagation of elements (Cartesian, Spherical, Keplerian or any one of the others) to determine landing site latitude and longitude in this program? I basically need to visualize how EDL is happening with a celestial spherical body in context.

Background:
My project is on the investigation of autonomous GNC in EDL (currently for airless body or the Moon), much like (ALHAT, Lander Vision System and other contemporary names given for AGNC with HDA). So, we've used University of Dundee's PANGU for surface and feature generation, DEM synthesis and utilizing slope/altitude maps fo Hazard detection part.

On the guidance part, I intend to integrate three distinct acceleration command profiles for braking (linear acceleration), approach (quadratic acceleration) and vertical descent as described in this work, taken from this reference by Ronald Sostaric. It seems far-fetched at this point when I'm struggling with above mentioned problem, but I'm trying.

Although I'll ask the questions here along the way as and when problems pop up, I would want SE experts to give their opinion or suggestion on anything of their interest.

One of the major problems with project is, that review panel is relatively unfamiliar with space technology and exploration. So, visualization is important for expressing the work done. Irrespective of whether panel is able to appreciate, I want to honestly work on the investigation and pull off a relevant study and learning in the remainder of next 3 months as I have done for past two. So, any and every view and response on any part is appreciated.